I've seen mention of these bugs, but have seen no response from Skype or any suggestion of fixes.
1) The most severe problem is that if you manage to get into the messaging screen in the full screen mode, i.e., no 2nd window on the left, you can never leave. There is no way to close the window, or return to any other skype activity. I found that even getting another message from another contact didn't help - I heard the beep, but couldn't leave the screen I was stuck on. Only way out is to leave Skype and uninstall it.
2) With so many install/uninstalls, sometimes the Skype icon would not even reappear. Some poor soul mentioned this and later said nevermind, it showed up when I installed another app. Well, I was able to power off and on and find the icon too, but neither of those options is a fix.
Like many others, I will leave Skype uninstalled from my iPad2 until these bugs are fixed.